{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:BK5FUHIKO6JR3E2BMYJEA76REL","short_pith_number":"pith:BK5FUHIK","canonical_record":{"source":{"id":"2603.20483","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-03-20T20:28:25Z","cross_cats_sorted":["cs.NA","math.PR"],"title_canon_sha256":"fd4311926d420e17d9b5d378117136053f1fb077b0ae61476c47a8a027bb22b1","abstract_canon_sha256":"46725d548f83194780d54b885e81c82934302cd00468ed18dc47ba6c1d486d10"},"schema_version":"1.0"},"canonical_sha256":"0aba5a1d0a77931d93416612407fd122eec444532d76f9b454853e614d6e025f","source":{"kind":"arxiv","id":"2603.20483","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.20483","created_at":"2026-06-19T16:10:36Z"},{"alias_kind":"arxiv_version","alias_value":"2603.20483v2","created_at":"2026-06-19T16:10:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.20483","created_at":"2026-06-19T16:10:36Z"},{"alias_kind":"pith_short_12","alias_value":"BK5FUHIKO6JR","created_at":"2026-06-19T16:10:36Z"},{"alias_kind":"pith_short_16","alias_value":"BK5FUHIKO6JR3E2B","created_at":"2026-06-19T16:10:36Z"},{"alias_kind":"pith_short_8","alias_value":"BK5FUHIK","created_at":"2026-06-19T16:10:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:BK5FUHIKO6JR3E2BMYJEA76REL","target":"record","payload":{"canonical_record":{"source":{"id":"2603.20483","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-03-20T20:28:25Z","cross_cats_sorted":["cs.NA","math.PR"],"title_canon_sha256":"fd4311926d420e17d9b5d378117136053f1fb077b0ae61476c47a8a027bb22b1","abstract_canon_sha256":"46725d548f83194780d54b885e81c82934302cd00468ed18dc47ba6c1d486d10"},"schema_version":"1.0"},"canonical_sha256":"0aba5a1d0a77931d93416612407fd122eec444532d76f9b454853e614d6e025f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:36.566577Z","signature_b64":"Hvu9AiyRhzVA4879jcy773P10M0qHxHskag5Uh3MIJVSai3jYmfgZHOdWbjjd7z4+ff8j+8HpqCmuceJdzLvBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0aba5a1d0a77931d93416612407fd122eec444532d76f9b454853e614d6e025f","last_reissued_at":"2026-06-19T16:10:36.566142Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:36.566142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.20483","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:10:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WY0kywJyEbS+QlWDqK34OapeWJ6RgYd/7+j39XC8xFuM4gn+L9zj2HqxCTTDt6HusKa4E1Sx/uDRcQA2TBe8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T10:52:06.398790Z"},"content_sha256":"d6c666028d7d7435d27779063d2efcd4a2b556f470d98312e9c5fbbf9a7cc107","schema_version":"1.0","event_id":"sha256:d6c666028d7d7435d27779063d2efcd4a2b556f470d98312e9c5fbbf9a7cc107"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:BK5FUHIKO6JR3E2BMYJEA76REL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence Analysis of the Random Bisection Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.PR"],"primary_cat":"math.NA","authors_text":"Ludovick Bouthat, Philippe-Andr\\'e Luneau, Philippe Petitclerc","submitted_at":"2026-03-20T20:28:25Z","abstract_excerpt":"We propose a generalized version of the bisection method where the cutting point between the two subintervals is chosen at random following an arbitrary distribution. We compute expected convergence rates with respect to any arbitrary a priori distribution for the position of the root in the initial interval and proved that it depends only on the the expectation $\\mathbb{E}[c(1-c)]$ of the cut $c$. We also provide a generalization of the method for $K$ random cuts and study its convergence properties. Most probabilistic derivations are kept fairly simple for the ease of understanding of a larg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.20483","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.20483/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:10:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+DUQpkfAAMaGM5EfV3r+gS/QUbdMbGaoBpVfqVMrP9W6ZChyEU2/tF/xxvA6h79QMJZWfk8RbUANj/cRJ6XaBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T10:52:06.399147Z"},"content_sha256":"8a77b506cc4b7e8e92244f2b4cba2871b3bbf2313aa7022d016a4aae22dbe0fc","schema_version":"1.0","event_id":"sha256:8a77b506cc4b7e8e92244f2b4cba2871b3bbf2313aa7022d016a4aae22dbe0fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BK5FUHIKO6JR3E2BMYJEA76REL/bundle.json","state_url":"https://pith.science/pith/BK5FUHIKO6JR3E2BMYJEA76REL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BK5FUHIKO6JR3E2BMYJEA76REL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-29T10:52:06Z","links":{"resolver":"https://pith.science/pith/BK5FUHIKO6JR3E2BMYJEA76REL","bundle":"https://pith.science/pith/BK5FUHIKO6JR3E2BMYJEA76REL/bundle.json","state":"https://pith.science/pith/BK5FUHIKO6JR3E2BMYJEA76REL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BK5FUHIKO6JR3E2BMYJEA76REL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BK5FUHIKO6JR3E2BMYJEA76REL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"46725d548f83194780d54b885e81c82934302cd00468ed18dc47ba6c1d486d10","cross_cats_sorted":["cs.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-03-20T20:28:25Z","title_canon_sha256":"fd4311926d420e17d9b5d378117136053f1fb077b0ae61476c47a8a027bb22b1"},"schema_version":"1.0","source":{"id":"2603.20483","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.20483","created_at":"2026-06-19T16:10:36Z"},{"alias_kind":"arxiv_version","alias_value":"2603.20483v2","created_at":"2026-06-19T16:10:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.20483","created_at":"2026-06-19T16:10:36Z"},{"alias_kind":"pith_short_12","alias_value":"BK5FUHIKO6JR","created_at":"2026-06-19T16:10:36Z"},{"alias_kind":"pith_short_16","alias_value":"BK5FUHIKO6JR3E2B","created_at":"2026-06-19T16:10:36Z"},{"alias_kind":"pith_short_8","alias_value":"BK5FUHIK","created_at":"2026-06-19T16:10:36Z"}],"graph_snapshots":[{"event_id":"sha256:8a77b506cc4b7e8e92244f2b4cba2871b3bbf2313aa7022d016a4aae22dbe0fc","target":"graph","created_at":"2026-06-19T16:10:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2603.20483/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a generalized version of the bisection method where the cutting point between the two subintervals is chosen at random following an arbitrary distribution. We compute expected convergence rates with respect to any arbitrary a priori distribution for the position of the root in the initial interval and proved that it depends only on the the expectation $\\mathbb{E}[c(1-c)]$ of the cut $c$. We also provide a generalization of the method for $K$ random cuts and study its convergence properties. Most probabilistic derivations are kept fairly simple for the ease of understanding of a larg","authors_text":"Ludovick Bouthat, Philippe-Andr\\'e Luneau, Philippe Petitclerc","cross_cats":["cs.NA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-03-20T20:28:25Z","title":"Convergence Analysis of the Random Bisection Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.20483","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d6c666028d7d7435d27779063d2efcd4a2b556f470d98312e9c5fbbf9a7cc107","target":"record","created_at":"2026-06-19T16:10:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"46725d548f83194780d54b885e81c82934302cd00468ed18dc47ba6c1d486d10","cross_cats_sorted":["cs.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-03-20T20:28:25Z","title_canon_sha256":"fd4311926d420e17d9b5d378117136053f1fb077b0ae61476c47a8a027bb22b1"},"schema_version":"1.0","source":{"id":"2603.20483","kind":"arxiv","version":2}},"canonical_sha256":"0aba5a1d0a77931d93416612407fd122eec444532d76f9b454853e614d6e025f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0aba5a1d0a77931d93416612407fd122eec444532d76f9b454853e614d6e025f","first_computed_at":"2026-06-19T16:10:36.566142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:36.566142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hvu9AiyRhzVA4879jcy773P10M0qHxHskag5Uh3MIJVSai3jYmfgZHOdWbjjd7z4+ff8j+8HpqCmuceJdzLvBw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:36.566577Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.20483","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6c666028d7d7435d27779063d2efcd4a2b556f470d98312e9c5fbbf9a7cc107","sha256:8a77b506cc4b7e8e92244f2b4cba2871b3bbf2313aa7022d016a4aae22dbe0fc"],"state_sha256":"1f4c132f8b79be9b42142b73706b98604a0669905e98e9c6057829dc1a84025d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ozV3EQ4vqw/dDJkDdnZlL9SZoqg4PnR90mtau4h5vMnmkPgAg8+o/N4aZX3QQ+MG1eQcLSZC1m4vXDrfbLsWCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T10:52:06.401003Z","bundle_sha256":"cd6c4fd7393371d8130a5693d9a169696e1b963c78a788d910bff70ce260ba05"}}